Let k₁,..., km be m (positive) natural numbers. Let D be an open disk and let z₁, ..., Zm be m distinct points in D. Suppose that g, h: DC are holomorphic functions that are nowhere 0 and consider the function f D\ {21,..., Zm} → C defined by : g(z) (z − 2₁)k¹ ... (z — Zm)km 1. What is the type of singularity at ze? Here is any index between 1 and m. 2. What is the residue at ze? Justify your answer carefully. f(z) =h(z) +
Let k₁,..., km be m (positive) natural numbers. Let D be an open disk and let z₁, ..., Zm be m distinct points in D. Suppose that g, h: DC are holomorphic functions that are nowhere 0 and consider the function f D\ {21,..., Zm} → C defined by : g(z) (z − 2₁)k¹ ... (z — Zm)km 1. What is the type of singularity at ze? Here is any index between 1 and m. 2. What is the residue at ze? Justify your answer carefully. f(z) =h(z) +
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter4: Vector Spaces
Section4.3: Subspaces Of Vector Spaces
Problem 49E
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![Let k₁,..., km be m (positive) natural numbers. Let D be an open disk and let 2₁,..., zm be m distinct
points in D. Suppose that g, h : D → C are holomorphic functions that are nowhere 0 and consider the
function f D\ {21,..., Zm} → C defined by
f(2)=h(z) +
g(z)
(z — 2₁) k₁... (z — Zm) km
1. What is the type of singularity at zę? Here l is any index between 1 and m.
2. What is the residue at ze? Justify your answer carefully.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7a04a0c8-a6a9-473e-b4ed-0840bde177a1%2Fcebd8004-535a-4faa-8902-f2f79b4f306c%2Fwm6gfj4_processed.png&w=3840&q=75)
Transcribed Image Text:Let k₁,..., km be m (positive) natural numbers. Let D be an open disk and let 2₁,..., zm be m distinct
points in D. Suppose that g, h : D → C are holomorphic functions that are nowhere 0 and consider the
function f D\ {21,..., Zm} → C defined by
f(2)=h(z) +
g(z)
(z — 2₁) k₁... (z — Zm) km
1. What is the type of singularity at zę? Here l is any index between 1 and m.
2. What is the residue at ze? Justify your answer carefully.
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